臺灣博碩士論文加值系統

本篇論文基於密度泛函理論，利用全位勢線性擴增平面波 (FLAPW) 及其廣義梯度近似法 (GGA) 的能帶計算方法。研究了一系列有關過渡金屬化合物的電子結構及其相關物理性質，其結果與實驗值以及其他的理論作比較與討論。
第一部份關於Ni3Al、Ni3Ga和Ni3In的晶格常數、體彈性模量、X光近邊緣吸收光譜 (XANES) 和光學性質的理論研究皆與實驗值相當吻合。理論發現這三個化合物都有相似的能帶結構，且皆呈現弱磁性。因為XANES實驗光譜被視為探測這些金屬間化合物的電子結構的有用工具，所以可藉由XANES的理論光譜和Ni p軌域的未佔據態態密度來分析實驗所量測的Ni K-edge的XANES光譜。然而，由於Ni3In的Ni K-edge XANES的理論與實驗光譜有些許差異，且其結構與磁性存有爭議。因此，對Ni3In進行三種類似結構(立方體L12、四方體D022與六方體D019)計算，其結果顯示Ni3In在低溫時呈現弱鐵磁性的L12結構，而當溫度上升至室溫時Ni3In會經歷磁性與結構的相變，並且也預測了在低溫而壓力為128 kbars時會引發L12到D022結構的相變，這與Ni3Al及其它相關合金不同。希望這些有趣的理論發現能有助於實驗上的探索，如近乎微弱磁性的化合物與其溫度相關的結構、比熱和磁化等實驗。
對另一系列材料：Fe3Al、Fe2VAl和Fe2VGa的晶體結構、體彈性模量、XANES光譜和磁學特性的理論研究皆與實驗值相當一致。理論與實驗都證實了Fe2VAl和Fe2VGa（皆為L21結構）皆為非磁性次金屬(semi-metal) 材料，而Fe3Al（為D03結構）則為鐵磁性金屬，因此磁性與它的結構有很大的關聯。由於XANES光譜的理論與實驗值幾乎一致，而且實驗的K-edge XANES光譜樣貌其實就是反映出這些金屬間化合物的Fe- 和V-p軌域的未占據狀態密度 (DOS)，因此證明了實驗量測上的精確度以及使用FLAPW理論方法及其GGA近似法去探討這些材料是適當的、可靠的。
另外最後我們以一個14.32 Å厚度的超晶胞薄片來模擬CeCo2奈米粒，並以GGA和GGA+U的方式來執行計算，兩者的理論結果在定性上與實驗所量測的奈米粒皆同樣具有磁性存在。然而，相較於CeCo2塊材其理論與實驗皆證實為無磁性的。因此，揭示了在觀察CeCo2奈米粒的磁性時其表面效應的確扮演了極重要的角色。
綜合上述，本論文以第一原理能帶理論對上述的過渡金屬化合物所做的一切關於材料性質的計算，所得的結果在定量上和定性上與已有的實驗值都相當的符合。希望這些詳盡完整的能帶計算結果有助於這些材料的微觀理論機理能有更清楚、深入的瞭解，此外，也希望對這些材料在未來的科技應用與發展有所貢獻。

In this thesis, we used full-potential linearized augmented-plane-wave method (FLAPW), and generalized gradient approximation (GGA) based on first-principles density-functional theory (DFT), to study the electronic structure and relative physical properties of a series of transition metals. The results are compared and discussed to the experimental values and other theories.
In the first part, we calculated lattice constants, bulk modulii, X-ray absorption near-edge spectra (XANES) and optical properties of Ni3Al, Ni3Ga and Ni3In, which are in good agreement with experiments. It is predicted that all three compounds have similar band structures and weak ferromagnetic. The measured Ni K-edge XANES are well explained by the theoretical XANES and unoccupied Ni-p density of states (DOS), suggesting that XANES is a useful probe of the electronic structure of the intermetallics. However, due to a small difference between theory and experimental Ni K-edge XANES spectra in Ni3In, there are still issues in its structure and magnetism. Therefore, we have carried out three similar structure calculations for Ni3In in the cubic L12, tetragonal D022 and hexagonal D019 structures. It is predicted that Ni3In would be a weak ferromagnet in the L12 structure at low temperatures and would become a paramagnet with the D022 structure as the temperature is increased to room temperature or above. It is also predicted that under high pressures of 128 kbars, Ni3In would undergo the same phase transition at low temperatures. This is different to Ni3Al and other relative compounds .We hope that these interesting theoretical findings would stimulate further experimental investigations such as temperature-dependent structural, specific-heat, and magnetization experiments on this nearly or weakly magnetic intermetallic compound.
For another series of materials, such as Fe3Al, Fe2VAl and Fe2VGa the theoretical studies of crystal structures, bulk modulii, XANES spectra and magnetic properties are in agreement with experiments. Both theories and experiments have proved that Fe2VAl and Fe2VGa (both are L21 structure) are nonmagnetic semi-metal. On the other hand, the Fe3Al (D03 structure) is a ferromagnetic metal. Therefore the magnetism has huge dependence on its structures. Because the theory of XANES spectra is almost consistent to the experiments, and the experimental XANES features for these intermetallic compounds reflect the Fe- and V-p unoccupied partial DOS. This proves that the precision of experimental measurement, and using FLAPW method and GGA to study these materials are reliable.
Finally, we simulate CeCo2 nano-particle for a supercell slab with a 14.32 Å thickness, and using GGA and GGA+U method to perform the calculation. Qualitatively, both results and measurement of nano-particle all possess magnetism. However, from theories and experiments, the bulk CeCo2 does not possess magnetism. Therefore, this suggests that surface effect may play a significant role in the magnetism observed in the nano-particle.
In summary, in this thesis we use first-principle to perform calculations on material properties of above transition metals. The results are in good agreement with experiments. We hope that these detailed calculations on band structures are useful for clearer, deeper understanding to microscopic properties of these materials. We also hope that these materials will have contributions to the development of technologically in the future.

圖目 ……………………………………………………………………..3
表目 ……………………………………………………………………..5
第一章 引言 ……………………………………………………………6
第二章 能帶理論與計算方法 ………………………………………..10
2-1何謂第一原理 ……………………………………………..10
2-2由密度泛函理論解釋量子多體問題 ……………………..12
2-2-1 Born-Oppenheimer近似 ……………………………...12
2-2-2 Hohenberg-Kohn原理 ………………………………..13
2-2-3 Kohn-Sham方程式 …………………………………...15
2-2-4 交換關聯泛函之近似 ………………………………..18
2-2-5 解晶體電子本微方程 ………………………………..19
2-3 簡介APW，LAPW和FLAPW方法 …………………..20
2-3-1 擴增平面波方法 (APW method) …………………….21
2-3-2 線性擴增平面波方法 (LAPW method)………………22
2-3-3 全位勢 (Full-Potential) 線性擴增平面波方法 (FLAPW method)及所有電子(all-electron)計算 …..23
2-3-4 結語 …………………………………………………..27
2-4 簡介X光輻射(吸收)光譜XES(XAS)之計算方法 ……...27
2-5 簡介光學性質之計算方法 ……………………………...31
2-6 簡介自旋極化與LDA+U計算方法 …..…………….......34
第三章 Ni3Al、Ni3Ga和Ni3In之理論與實驗研究 …………………41
3-1 結構簡介與計算細節 …………………………………….41
3-2 理論與實驗之結果分析 ………………………………….43
3-2-1 電子能帶與磁學性質 ………………………………..44
3-2-2 X光近邊緣吸收光譜 ………………………………..49
3-2-3 光學性質 ……………………………………………..52
3-3 重新探討Ni3In的穩定結構及磁性 ……………………...58
3-3-1 結構簡介與計算細節 ………………………………..59
3-3-2 討論晶體結構的穩定性 ……………………………..61
3-3-3 電子能帶與磁學性質 ………………………………..65
3-3-4 理論與實驗的光譜之比較 …………………………..71
第四章 Fe3Al、Fe2VAl和Fe2VGa之理論與實驗研究 …………….75
4-1 結構簡介與計算細節 …………………………………….75
4-2 理論與實驗之結果分析 ………………………………….78
第五章 探討CeCo2的塊材與奈米粒之電子結構及磁性 …………..84
5-1 結構簡介與計算細節 …………………………………….84
5-2 結果與討論 ……………………………………………….86
第六章 結論與展望 ..............................................................................90
參考文獻 ………………………………………………………………95
攻讀博士學位期間發表和待發表的文章 …………………………..101

1. Born M. and Hunang K., Dynamical Theory of Crystal Lattices. Oxford: Oxford University Press, (1954).
2. Neil W. Ashcroft and N. David Mermin, Solid State Physics, Cornell University, (1976).
3. Otfried Madelung, Introduction to Solid-State Theory, Marburg University, Germany (Springer, 1996).
4. Charles Kittel, Introduction to Solid State Physics, Wiley USA, (1996).
5. 謝希德、陸棟，固體能帶理論，復旦大學出版社，(1998).
6. 黃昆，韓汝琦，固體物理學，高等教育出版社 (1988)
7. Thomas H., Proc. Camb. Phil. Soc., 23 (1927) 542.
8. Fermi E., Accad. Naz. Lincei, 6 (1927) 602.
9. Hohenberg P. and Kohn W., Phys. Rev. 136 (1964) B864.
10. Kohn W. and Sham L. J., Phys. Rev. 140 (1965) A1133; Fock V. Z. Phys. 61 (1930) 209
11. Wigner, E. P., Phys. Rev. 46 (1934) 1002.
12. Hedin, L., and B. I. Lundqvist, J. Phys. C4 (1971) 2064.
13. Perdew J. P. and Wang Y., Phys. Rev. B 45 (1992) 13244.
14. Perdew J. P., Burke S. and Ernzerhof M. Phys. Rev. Let. 77 (1996) 3865.
15. Slater J. C., Phys. Rev. 51 (1937) 846; 92 (1953) 603.
16. Loucks T. L., Augmented Plane Wave Method. New York, W. A. Benjamin Inc. (1967).
17. D. D. Koeling and G. O. Arbman, J. Phys. F 5 (1975) 2041.
18. O. K. Andersen, Phys. Rev. B 12 (1975) 3060.
19. E. Wimmer, H. Krakauer, M. Weinert and A. J. Freeman, Phys. Rev. B 24 (1981) 864.
20. Pratt G. W. Phys. Rev. 88 (1952) 1217.
21. A. Neckel, K. Schwarz, R. Eibler and P. Rastl, Microchim. Acta, Suppl. 6 (1975) 257.
22. K. Schwarz, A. Neckel, J Nordgren, J. Phys. F : Metal Phys. 9 (1979) 2509.
23. K. Schwarz, E. Wimmer, J. Phys. F : Metal Phys. 10 (1980) 1001.
24. E. J. Mcguire Phys. Rev. A2 (1970) 273; A3 (1971) 587; A5 (1972) 1043.
25. M. A. Blokhin, W. P. Sachenko, Izv. Akad. Nauk. SSSR Ser. 2 Fiz. 24 (1960) 397.
26. R. D. Sole and R. Girlanda, Phys. Rev. B 48 (1994) l l789.
27. M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 81 (1998) 2312.
28. C. Ambrosch-Draxl and R. Abt, Synth. Met 85 (1997) l099.
29. Z. H. Levine and D. C. Allan, Phys. Rev. Lett. 63 (1989) 1719.
30. R. W. Godby, M. Schluter and L. J. Sham, Phys. Rev. B 37 (1988) 10159.
31. P. E. Blochl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49 (1994) 16223.
32. M. T. Czyzyk and G. A. Sawatzky, Phys. Rev. B 49 (1994) 14211.
33. V. I. Anisimov, I. V. Solovyev, M. A. Korotin, M. T. Czyzyk, and G. A. Sawatzky, Phys. Rev. B 48 (1993) 16929.
34. I. V. Solovyev, P. H. Dederichs, and V. I. Anisimov, Phys. Rev. B 50 (1994) 16861.
35. A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52 (1995) 5467.
36. A. B. Shick, A. I. Liechtenstein, and W. E. Pickett, Phys. Rev. B 60 (1999) 10763.
37. D. J. Singh, Planewaves, pseudopotentials and the LAPW method (Kluwer Academic, Dordrecht, 1994).
38. G. Y. Guo, Y. K. Wang and L.-S. Hsu, J. Magn. Magn. Mater. 239 (2002) 91-93.
39. L.-S. Hsu, Y. K. Wang and G. Y. Guo, J. Appl. Phys. 92 (2002) 1419.
40. F. R. de Boer, et al., J. Appl. Phys. 40 (1969) 1049.
41. N. Shiotani, C. R. Bull, R. N. West, N. Kawamiya, Y. Kubo, and S. Wakoh, J. Phys. Soc. Jpn. 55 (1986) 1961.
42. N. R. Bernhoeft, G. G. Lonzarich, P. W. Mitchell, and D. Mck. Paul, Phys. Rev. Lett. 62 (1989) 657.
43. H. Yasuda, T. Takasugi, M. Koiwa, Acta Metall. Mater. 40 (1992) 381.
44. L.-S. Hsu, R.S. Williams, J. Phys. Chem. Solids 55 (1994) 305.
45. A. N. Mansour, A. Dmitrienko, A. V. Soldatov, Phys. Rev. B 55 (1997) 15531.
46. Y. K. Chang, K. P. Lin, W. F. Pong, M.-H. Tsai, H. H. Hsieh, J. Y. Pieh, P. K. Tseng, J. F. Lee, and L.-S. Hsu, J. Appl. Phys. 87 (2000) 1312.
47. B. I. Min, A. J. Freeman, H. J. F. Jansen, Phys. Rev. B 37 (1988) 6757.
48. D. Iotova, N. Kioussis, S.P. Lim, Phys. Rev. B 54 (1996) 14413.
49. P. Blaha, K. Schwarz, and J. Luitz, WIEN97 (Vienna Univ. of Technology, Vienna, 1997); P. Blaha, K. Schwarz, and J. Luitz, [Improved and updated UNIX version of the original copyrighted WIEN code, which was published by P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, Comput. Phys. Commun. 59, 399 (1990)].
50. F. D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 3 (1944) 244.
51. F. Wallow, G. Neite, W. Schroer, and E. Nembach, Phys. Status Solidi A 99 (1987) 483.
52. F. X. Kayser and C. Stassis, Phys. Status Solidi A 64 (1981) 335.
53. N. Buis, J. J. M. Franse, and P. E. Brommer, Physica B & C 106B (1981) 1.
54. V. L. Moruzzi and P. M. Marcus, Phys. Rev. B 42 (1990) 5539, and references therein.
55. B. I. Min, T. Oguchi, H. J. F. Jansen, and A. J. Freeman, J. Magn. Magn. Mater. 54—57 (1986) 1091; J.-H. Xu, T. Oguchi, and A. J. Freeman, Phys. Rev. B 36 (1987) 4186; J.-H. Xu, B. I. Min, A. J. Freeman, and T. Oguchi, Phys. Rev. B 41 (1990) 5010.
56. W. de Dood and P. F de Chatel, J. Phys. F: Met. Phys. 3 (1973) 1039.
57. J. C. Ho, R. C. Liang, and D. P. Dandekar, J. Appl. Phys. 59 (1986) 1397.
58. C. Stassis, F. X. Kayser, C.-K. Loong, and D. Arch, Phys. Rev. B 24 (1981) 3048.
59. D. Hackenbracht and J. Kubler, J. Phys. F: Met. Phys. 10 (1980) 427.
60. B. I. Min, A. J. Freeman, and H. J. F. Jansen, Phys. Rev. B 37 (1988) 6757.
61. G. C. Fletcher, Physica (Amsterdam) 62 (1972) 41.
62. J. J. M. Buiting, J. Kubler, and F. M. Mueller, J. Phys. F: Met. Phys. 13 (1983) L179.
63. Y. Kubo and S. Wakoh, J. Phys. F: Met. Phys. 17 (1987) 397.
64. E. Fawcett, J. P. Maita, E. Bucher, and J. H. Wernick, Phys. Rev. B 2 (1970) 3639 .
65. L.-S. Hsu, K.-L. Tsang, and S.-C. Chung, in Applications of Synchrotron Radiation Techniques to Materials Science III, edited by L. J. Terminello, S. M. Mini, H. Ade, and D. L. Perry, Mater. Res. Soc. Symp. Proc. No. 437 (Materials Research Society, Pittsburgh, 1996), p. 53.
66. W. F. Pong, K. P. Lin, Y. K. Chang, M.-H. Tsai, H. H. Hsieh, J. Y. Pieh, P. K. Tseng, J. F. Lee, and L.-S. Hsu, J. Synchrotron Radiat. 6 (1999) 731.
67. L.-S. Hsu, K.-L. Tsang, and S.-C. Chung, J. Magn. Magn. Mater. 177—181 (1998) 1031.
68. J. P. Perdew, S. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.
69. D. A. Muller, S. Subramanian, P. E. Batson, S. L. Sass, and J. Silcox, Phys. Rev. Lett. 75 (1995) 4744.
70. S. J. Pickart and R. Nathans, Phys. Rev. 123 (1961) 1163
71. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys (American Society of Metals, Metals Park, OH, 1973).
72. Smirthells Metals Reference Book, 6th ed., edited by E. A. Brandes (Butterworths, London, 1983).
73. O. Kubaschewski, E. L. Evans, and C. B. Alcock, Metallurgical Thermochemistry, 4th ed. (Pergamon, Oxford, 1979).
74. P. Horsch, W. von der Linden, and W.-D. Lukas, Solid State Commun. 62 (1978) 359.
75. P. A. M. van der Heide, J. J. M. Buiting, L. M. ten Dam, L. W. M. Schreurs, R. A. de Groot, and A. R. de Vroomen, J. Phys. F 15 (1985) 1195.
76. J. Y. Rhee, Y. V. Kudryavtsev, and Y. P. Lee, Phys. Rev. B68 (2003) 045104.
77. M. A. Khan, A. Kashyap, A. K. Solanki, T. Nautiyal, and S. Auluck, Phys. Rev. B48 (1993) 16974.
78. J. Y. Rhee, B. N. Harmon, and D. W. Lynch, Phys. Rev. B55 (1997) 4124.
79. P. M. Oppeneer, T. Maurer, J. Sticht and J. Kubler, Phys. Rev. B45 (1992) 10924.
80. Anna Delin, Olle Eriksson, Borje Johansson, Sushil Auluck and J. M. Wills, Phys. Rev. B60 (1999) 14105.
81. Kwang Joo Kim, T. C. Leung, B. N. Harmoon and D. W. Lynch, J. Phys. :Condens. Matter 6 (1994) 5069.
82. G. Y. Guo, Y. K. Wang and L.-S. Hsu, Phys. Rev. B 66 (2002) 054440.
83. W.B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys (Pergamon, New York, 1958).
84. R. V. Baranova, Kristallografiya 10 (1965) 32 [Sov. Phys. Crystallogr. 10, 24 (1965)].
85. L.-S. Hsu, Ph. D. thesis, Univ. of California, Los Angeles, 1988.
86. L.-S. Hsu, G.-H. Gweon, and J.W. Allen, J. Phys. Chem. Solids 60 (1999) 1627.
87. L.-S. Hsu, K.-L. Tsang, and S.-C. Chung, Int. J. Mod. Phys. B 12 (1998) 26.
88. L.-S. Hsu and A. I. Nesvizhskii, J. Phys. Chem. Solids 62 (2001) 1103.
89. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, and J. Luitz et al., WIEN2K, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universitat Wien, Austria), 2001. ISBN 3-9501031-1-2.
90. G. Y. Guo and H. H. Wang, Chin. J. Phys. (Taipei) 38 (2000) 949.
91. J. F. Janak, Phys. Rev. B 16 (1977) 255.
92. M. S. S. Brooks, O. Eriksson, B. Johansson, J. J. M. Franse, and P. H. Frings, J. Phys. F: Met. Phys. 18 (1988) L33.
93. G.Y. Guo and H. H. Wang, Phys. Rev. B 62 (2000) 5136.
94. L.-S. Hsu, Y. K. Wang and G. Y. Guo, Phys. Rev. B 66 (2002) 205203.
95. T. J. Burch, K. Raj, P. Jena, J. I. Budnick, V. Niculescu, and W. B. Muir, Phys. Rev. B 19 (1979) 2933.
96. Y. Nishino, M. Kato, S. Asano, K. Soda, M. Hayasaki, and U. Mizutani, Phys. Rev. Lett. 79 (1997) 1909.
97. K. Endo, H. Matsuda, K. Ooiwa, M. Iijima, K. Ito, T. Goto, and A. Ono, J. Phys. Soc. Jpn. 66 (1997) 1257; K. Endo, H. Matsuda, K. Ooiwa, M. Iijima, T. Goto, K. Sato, and I. Umehara, J. Magn. Magn. Mater. 177—181 (1998) 1437.
98. G. Y. Guo, G. A. Botton, and Y. Nishino, J. Phys.: Condens. Matter 10 (1998) L119.
99. D. J. Singh and I. I. Mazin, Phys. Rev. B 57 (1998) 14352.
100. R. Weht and W. E. Pickett, Phys. Rev. B 58 (1998) 6855.
101. M. Weinert and R. E. Watson, Phys. Rev. B 58 (1998) 9732.
102. A. Bansil, S. Kaprzyk, P. E. Mijnarends, and J. Tobola, Phys. Rev. B 60 (1999) 13396.
104. C.-S. Lue and J. H. Ross, Jr., Phys. Rev. B 58 (1998) 9763.
105. C. S. Lue and J. H. Ross, Jr., Phys. Rev. B 61 (2000) 9863.
106. H. Okamura, J. Kawahara, T. Nanba, S. Kimura, K. Soda, U. Mizutani, Y. Nishino, M. Kato, I. Shimoyama, H. Miura, K. Fukui, K. Nakagawa, H. Nakagawa, and T. Kinoshita, Phys. Rev. Lett. 84 (2000) 3674.
107. C.-S. Lue and J. H. Ross, Jr., Phys. Rev. B 63 (2001) 054420.
108. H. Okamoto and P. A. Beck, Monatsh. Chem. 103 (1972) 907.
109. R. Kuentzler, J. Phys. (Paris) 44 (1983) 1167.
110. S. Ishida, J. Ishida, S. Asano, and J. Yamashita, J. Phys. Soc. Jpn. 41 (1976) 1570 .
111. W. B. Muir, J. I. Budnick, and K. Raj, Phys. Rev. B 25 (1982) 726.
112. C. S. Lue, J. H. Ross, Jr., K. D. D. Rathnayaka, D. G. Naugle, S. Y. Wu, and W.-H. Li, J. Phys.: Condens. Matter 13 (2001) 1585.
113. S. J. Pickart and R. Nathans, Phys. Rev. 123 (1961) 1163.
114. R. Nathans, M. T. Pigott, and C. G. Shull, J. Phys. Chem. Solids 6 (1958) 38.
115. T. Wakiyama, J. Phys. Soc. Jpn. 32 (1972) 1222.
116. A. P. Malozemoff, A. R. Williams, V. L. Moruzzi, and K. Terakura, Phys. Rev. B 30 (1984) 6565.
117. G. Y. Guo, Y. K. Wang, and Y. Y. Chen, J. Magn. Magn. Mater. (2003 accepted).
118. T. M. Seixas, J. M. Machado Silva, Physica B 269 (1999) 362.
119. C. R. Wang, et al., J. Magn. Magn. Mater. 239 (2002) 524.
120. H. Sugawara, et al., J. Phys. Soc. Jpn. 65 (1996) 1744.